#include <deal.II/matrix_free/operators.h>

Inheritance diagram for MatrixFreeOperators::Base< dim, VectorType >:

Public Types
using	value_type = typename VectorType::value_type

using	size_type = typename VectorType::size_type

Public Member Functions
	Base ()

virtual	~Base () override=default

virtual void	clear ()

void	initialize (std::shared_ptr< const MatrixFree< dim, value_type >> data, const std::vector< unsigned int > &selected_row_blocks=std::vector< unsigned int >(), const std::vector< unsigned int > &selected_column_blocks=std::vector< unsigned int >())

void	initialize (std::shared_ptr< const MatrixFree< dim, value_type >> data, const MGConstrainedDoFs &mg_constrained_dofs, const unsigned int level, const std::vector< unsigned int > &selected_row_blocks=std::vector< unsigned int >())

void	initialize (std::shared_ptr< const MatrixFree< dim, value_type >> data_, const std::vector< MGConstrainedDoFs > &mg_constrained_dofs, const unsigned int level, const std::vector< unsigned int > &selected_row_blocks=std::vector< unsigned int >())

size_type	m () const

size_type	n () const

void	vmult_interface_down (VectorType &dst, const VectorType &src) const

void	vmult_interface_up (VectorType &dst, const VectorType &src) const

void	vmult (VectorType &dst, const VectorType &src) const

void	Tvmult (VectorType &dst, const VectorType &src) const

void	vmult_add (VectorType &dst, const VectorType &src) const

void	Tvmult_add (VectorType &dst, const VectorType &src) const

value_type	el (const unsigned int row, const unsigned int col) const

virtual std::size_t	memory_consumption () const

void	initialize_dof_vector (VectorType &vec) const

virtual void	compute_diagonal ()=0

std::shared_ptr< const MatrixFree< dim, value_type > >	get_matrix_free () const

const std::shared_ptr< DiagonalMatrix< VectorType > > &	get_matrix_diagonal_inverse () const

const std::shared_ptr< DiagonalMatrix< VectorType > > &	get_matrix_diagonal () const

void	precondition_Jacobi (VectorType &dst, const VectorType &src, const value_type omega) const

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

void	subscribe (const char *identifier=nullptr) const

void	unsubscribe (const char *identifier=nullptr) const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Protected Member Functions
void	preprocess_constraints (VectorType &dst, const VectorType &src) const

void	postprocess_constraints (VectorType &dst, const VectorType &src) const

void	set_constrained_entries_to_one (VectorType &dst) const

virtual void	apply_add (VectorType &dst, const VectorType &src) const =0

virtual void	Tapply_add (VectorType &dst, const VectorType &src) const

Protected Attributes
std::shared_ptr< const MatrixFree< dim, value_type > >	data

std::shared_ptr< DiagonalMatrix< VectorType > >	diagonal_entries

std::shared_ptr< DiagonalMatrix< VectorType > >	inverse_diagonal_entries

std::vector< unsigned int >	selected_rows

std::vector< unsigned int >	selected_columns

Private Member Functions
void	mult_add (VectorType &dst, const VectorType &src, const bool transpose) const

void	adjust_ghost_range_if_necessary (const VectorType &vec, const bool is_row) const

Private Attributes
std::vector< std::vector< unsigned int > >	edge_constrained_indices

std::vector< std::vector< std::pair< value_type, value_type > > >	edge_constrained_values

bool	have_interface_matrices

Additional Inherited Members
Static Public Member Functions inherited from Subscriptor
static::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Detailed Description

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>
class MatrixFreeOperators::Base< dim, VectorType >

Abstract base class for matrix-free operators which can be used both at the finest mesh or at a certain level in geometric multigrid.

A derived class has to implement apply_add() method as well as compute_diagonal() to initialize the protected member inverse_diagonal_entries and/or diagonal_entries. In case of a non-symmetric operator, Tapply_add() should be additionally implemented.

Currently, the only supported vectors are LinearAlgebra::distributed::Vector and LinearAlgebra::distributed::BlockVector.

Selective use of blocks in MatrixFree

MatrixFree allows to use several DoFHandler/AffineConstraints combinations by passing a std::vector with pointers to the respective objects into the MatrixFree::reinit function. This class supports to select only some of the blocks in the underlying MatrixFree object by optional integer lists that specify the chosen blocks.

One application of constructing a matrix-free operator only on selected blocks would be the setting of the step-32 tutorial program: This problem has three blocks, one for the velocity, one for the pressure, and one for temperature. The time lag scheme used for temporal evolution splits the temperature equation away from the Stokes system in velocity and pressure. However, there are cross terms like the velocity that enters the temperature advection-diffusion equation or the temperature that enters the right hand side of the velocity. In order to be sure that MatrixFree uses the same integer indexing to the different blocks, one needs to put all the three blocks into the same MatrixFree object. However, when solving a linear system the operators involved either address the first two in the Stokes solver, or the last one for the temperature solver. In the former case, a BlockVector of two components would be selected with a vector selecting the blocks {0, 1} in MatrixFree, whereas in the latter, a non-block vector selecting the block {2} would be used.

A second application of selection is in problems with a Newton-type iteration or problems with inhomogeneous boundary conditions. In such a case, one has to deal with two different sets of constraints: One set of constraints applies to the solution vector which might include hanging node constraints or periodicity constraints but no constraints on inhomogeneous Dirichlet boundaries. Before the nonlinear iteration, the boundary values are set to the expected value in the vector, representing the initial guess. In each iteration of the Newton method, a linear system subject to zero Dirichlet boundary conditions is solved that is then added to the initial guess. This setup can be realized by using a vector of two pointers pointing to the same DoFHandler object and a vector of two pointers to the two AffineConstraints objects. If the first constraint matrix is the one including the zero Dirichlet constraints, one would give a std::vector<unsigned int>(1, 0) to the initialize() function, i.e., a vector of length 1 that selects exactly the first constraint matrix with index 0.

For systems of PDEs where the different blocks of MatrixFree are associated with different physical components of the equations, adding another block with a different AffineConstraints argument solely for the purpose of boundary conditions might lead to cumbersome index handling. Instead, one could set up a second MatrixFree instance with the different constraint matrix but the same interpretation of blocks, and use that for interpolating inhomogeneous boundary conditions (see also the discussion in the results section of the step-37 tutorial program):

matrix_free_inhomogeneous.reinit(dof_handler, constraints_no_dirichlet,
                                 quadrature, additional_data);
operator_inhomogeneous.initialize(matrix_free_inhomogeneous,
                                  selected_blocks);
LinearAlgebra::distributed::Vector<double> inhomogeneity;
matrix_free_inhomogeneous.initialize_dof_vector(inhomogeneity);
constraints_with_dirichlet.distribute(inhomogeneity);
operator_inhomogeneous.vmult(system_rhs, inhomogeneity);
system_rhs *= -1.;
// proceed with other terms from right hand side...

Author: Denis Davydov, Daniel Arndt, Martin Kronbichler, 2016, 2017

Definition at line 187 of file operators.h.

Member Typedef Documentation

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

using MatrixFreeOperators::Base< dim, VectorType >::value_type = typename VectorType::value_type

Number alias.

Definition at line 193 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

using MatrixFreeOperators::Base< dim, VectorType >::size_type = typename VectorType::size_type

size_type needed for preconditioner classes.

Definition at line 198 of file operators.h.

Constructor & Destructor Documentation

template<int dim, typename VectorType >

MatrixFreeOperators::Base< dim, VectorType >::Base ( )

Default constructor.

Definition at line 1004 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

virtual MatrixFreeOperators::Base< dim, VectorType >::~Base ( )

overridevirtualdefault

Virtual destructor.

Member Function Documentation

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::clear ( )

virtual

Release all memory and return to a state just like after having called the default constructor.

Reimplemented in MatrixFreeOperators::LaplaceOperator< dim, fe_degree, n_q_points_1d, n_components, VectorType >.

Definition at line 1039 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

void MatrixFreeOperators::Base< dim, VectorType >::initialize	(	std::shared_ptr< const MatrixFree< dim, value_type >>	data,
		const std::vector< unsigned int > &	selected_row_blocks = `std::vector< unsigned int >()`,
		const std::vector< unsigned int > &	selected_column_blocks = `std::vector< unsigned int >()`
	)

Initialize operator on fine scale.

The optional selection vector allows to choose only some components from the underlying MatrixFree object, e.g. just a single one. The entry selected_row_blocks[i] in the vector chooses the DoFHandler and AffineConstraints object that was given as the selected_row_blocks[i]-th argument to the MatrixFree::reinit() call. Different arguments for rows and columns also make it possible to select non-diagonal blocks or rectangular blocks. If the row vector is empty, all components are selected, otherwise its size must be smaller or equal to MatrixFree::n_components() and all indices need to be unique and within the range of 0 and MatrixFree::n_components(). If the column selection vector is empty, it is taken the same as the row selection, defining a diagonal block.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

void MatrixFreeOperators::Base< dim, VectorType >::initialize	(	std::shared_ptr< const MatrixFree< dim, value_type >>	data,
		const MGConstrainedDoFs &	mg_constrained_dofs,
		const unsigned int	level,
		const std::vector< unsigned int > &	selected_row_blocks = `std::vector< unsigned int >()`
	)

Initialize operator on a level level for a single FiniteElement.

The optional selection vector allows to choose only some components from the underlying MatrixFree object, e.g. just a single one. The entry selected_row_blocks[i] in the vector chooses the DoFHandler and AffineConstraints object that was given as the selected_row_blocks[i]-th argument to the MatrixFree::reinit() call. Since a multigrid operator is always associated to inverting a matrix and thus represents a diagonal block, the same vector for rows and columns is used as opposed to the non-level initialization function. If empty, all components are selected.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::initialize	(	std::shared_ptr< const MatrixFree< dim, value_type >>	data_,
		const std::vector< MGConstrainedDoFs > &	mg_constrained_dofs,
		const unsigned int	level,
		const std::vector< unsigned int > &	selected_row_blocks = `std::vector<unsigned int>()`
	)

Initialize operator on a level level for multiple FiniteElement objects.

The optional selection vector allows to choose only some components from the underlying MatrixFree object, e.g. just a single one. The entry selected_row_blocks[i] in the vector chooses the DoFHandler and AffineConstraints object that was given as the selected_row_blocks[i]-th argument to the MatrixFree::reinit() call. Since a multigrid operator is always associated to inverting a matrix and thus represents a diagonal block, the same vector for rows and columns is used as opposed to the non-level initialization function. If empty, all components are selected.

Definition at line 1157 of file operators.h.

template<int dim, typename VectorType >

Base< dim, VectorType >::size_type MatrixFreeOperators::Base< dim, VectorType >::m ( ) const

Return the dimension of the codomain (or range) space.

Definition at line 1013 of file operators.h.

template<int dim, typename VectorType >

Base< dim, VectorType >::size_type MatrixFreeOperators::Base< dim, VectorType >::n ( ) const

Return the dimension of the domain space.

Definition at line 1026 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::vmult_interface_down	(	VectorType &	dst,
		const VectorType &	src
	)		const

vmult operator for interface.

Definition at line 1392 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::vmult_interface_up	(	VectorType &	dst,
		const VectorType &	src
	)		const

vmult operator for interface.

Definition at line 1444 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::vmult	(	VectorType &	dst,
		const VectorType &	src
	)		const

Matrix-vector multiplication.

Definition at line 1245 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::Tvmult	(	VectorType &	dst,
		const VectorType &	src
	)		const

Transpose matrix-vector multiplication.

Definition at line 1483 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::vmult_add	(	VectorType &	dst,
		const VectorType &	src
	)		const

Adding Matrix-vector multiplication.

Definition at line 1256 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::Tvmult_add	(	VectorType &	dst,
		const VectorType &	src
	)		const

Adding transpose matrix-vector multiplication.

Definition at line 1265 of file operators.h.

template<int dim, typename VectorType >

Base< dim, VectorType >::value_type MatrixFreeOperators::Base< dim, VectorType >::el	(	const unsigned int	row,
		const unsigned int	col
	)		const

Return the value of the matrix entry (row,col). In matrix-free context this function is valid only for row==col when diagonal is initialized.

Definition at line 1049 of file operators.h.

template<int dim, typename VectorType >

std::size_t MatrixFreeOperators::Base< dim, VectorType >::memory_consumption ( ) const

virtual

Determine an estimate for the memory consumption (in bytes) of this object.

Definition at line 1494 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::initialize_dof_vector ( VectorType & vec ) const

A wrapper for initialize_dof_vector() of MatrixFree object.

Definition at line 1064 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

virtual void MatrixFreeOperators::Base< dim, VectorType >::compute_diagonal ( )

pure virtual

Compute diagonal of this operator.

A derived class needs to implement this function and resize and fill the protected member inverse_diagonal_entries and/or diagonal_entries accordingly.

Implemented in MatrixFreeOperators::LaplaceOperator< dim, fe_degree, n_q_points_1d, n_components, VectorType >, and MatrixFreeOperators::MassOperator< dim, fe_degree, n_q_points_1d, n_components, VectorType >.

template<int dim, typename VectorType >

std::shared_ptr< const MatrixFree< dim, typename Base< dim, VectorType >::value_type > > MatrixFreeOperators::Base< dim, VectorType >::get_matrix_free ( ) const

Get read access to the MatrixFree object stored with this operator.

Definition at line 1506 of file operators.h.

template<int dim, typename VectorType >

const std::shared_ptr< DiagonalMatrix< VectorType > > & MatrixFreeOperators::Base< dim, VectorType >::get_matrix_diagonal_inverse ( ) const

Get read access to the inverse diagonal of this operator.

Definition at line 1515 of file operators.h.

template<int dim, typename VectorType >

const std::shared_ptr< DiagonalMatrix< VectorType > > & MatrixFreeOperators::Base< dim, VectorType >::get_matrix_diagonal ( ) const

Get read access to the diagonal of this operator.

Definition at line 1527 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

void MatrixFreeOperators::Base< dim, VectorType >::precondition_Jacobi	(	VectorType &	dst,
		const VectorType &	src,
		const value_type	omega
	)		const

Apply the Jacobi preconditioner, which multiplies every element of the src vector by the inverse of the respective diagonal element and multiplies the result with the relaxation factor omega.

Definition at line 1548 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::preprocess_constraints	(	VectorType &	dst,
		const VectorType &	src
	)		const

protected

Perform necessary operations related to constraints before calling apply_add() or Tapply_add() inside mult_add().

Definition at line 1312 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::postprocess_constraints	(	VectorType &	dst,
		const VectorType &	src
	)		const

protected

Perform necessary operations related to constraints after calling apply_add() or Tapply_add() inside mult_add().

Definition at line 1359 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::set_constrained_entries_to_one ( VectorType & dst ) const

protected

Set constrained entries (both from hanging nodes and edge constraints) of dst to one.

Definition at line 1227 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

virtual void MatrixFreeOperators::Base< dim, VectorType >::apply_add	(	VectorType &	dst,
		const VectorType &	src
	)		const

protectedpure virtual

Apply operator to src and add result in dst.

Implemented in MatrixFreeOperators::LaplaceOperator< dim, fe_degree, n_q_points_1d, n_components, VectorType >, and MatrixFreeOperators::MassOperator< dim, fe_degree, n_q_points_1d, n_components, VectorType >.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::Tapply_add	(	VectorType &	dst,
		const VectorType &	src
	)		const

protectedvirtual

Apply transpose operator to src and add result in dst.

Default implementation is to call apply_add().

Definition at line 1538 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::mult_add	(	VectorType &	dst,
		const VectorType &	src,
		const bool	transpose
	)		const

private

Function which implements vmult_add (transpose = false) and Tvmult_add (transpose = true).

Definition at line 1340 of file operators.h.

template<int dim, typename VectorType >

void MatrixFreeOperators::Base< dim, VectorType >::adjust_ghost_range_if_necessary	(	const VectorType &	vec,
		const bool	is_row
	)		const

private

Adjust the ghost range of the vectors to the storage requirements of the underlying MatrixFree class. This is used inside the mult_add() as well as vmult_interface_up() and vmult_interface_down() methods in order to ensure that the cell loops will be able to access the ghost indices with the correct local indices.

Definition at line 1275 of file operators.h.

Member Data Documentation

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

std::shared_ptr<const MatrixFree<dim, value_type> > MatrixFreeOperators::Base< dim, VectorType >::data

protected

MatrixFree object to be used with this operator.

Definition at line 427 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

std::shared_ptr<DiagonalMatrix<VectorType> > MatrixFreeOperators::Base< dim, VectorType >::diagonal_entries

protected

A shared pointer to a diagonal matrix that stores the diagonal elements as a vector.

Definition at line 433 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

std::shared_ptr<DiagonalMatrix<VectorType> > MatrixFreeOperators::Base< dim, VectorType >::inverse_diagonal_entries

protected

A shared pointer to a diagonal matrix that stores the inverse of diagonal elements as a vector.

Definition at line 439 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

std::vector<unsigned int> MatrixFreeOperators::Base< dim, VectorType >::selected_rows

protected

A vector which defines the selection of sub-components of MatrixFree for the rows of the matrix representation.

Definition at line 445 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

std::vector<unsigned int> MatrixFreeOperators::Base< dim, VectorType >::selected_columns

protected

A vector which defines the selection of sub-components of MatrixFree for the columns of the matrix representation.

Definition at line 451 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

std::vector<std::vector<unsigned int> > MatrixFreeOperators::Base< dim, VectorType >::edge_constrained_indices

private

Indices of DoFs on edge in case the operator is used in GMG context.

Definition at line 457 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

std::vector<std::vector<std::pair<value_type, value_type> > > MatrixFreeOperators::Base< dim, VectorType >::edge_constrained_values

mutableprivate

Auxiliary vector.

Definition at line 463 of file operators.h.

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>

bool MatrixFreeOperators::Base< dim, VectorType >::have_interface_matrices

private

A flag which determines whether or not this operator has interface matrices in GMG context.

Definition at line 469 of file operators.h.

The documentation for this class was generated from the following file:

deal.II/matrix_free/operators.h

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>> class MatrixFreeOperators::Base< dim, VectorType >

Selective use of blocks in MatrixFree

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<int dim, typename VectorType = LinearAlgebra::distributed::Vector<double>>
class MatrixFreeOperators::Base< dim, VectorType >